The reliability of control systems, in particularly of temperature control loops, essentially depends on the accurate performance of its individual components forming the control loop, such as the actual value sensor, the controller and the final control element. The performance may be monitored e.g. by a second measuring circuit consisting of a second measuring sensor which is connected to an independent monitoring device for the actual value of the controlled quantity. If a permitted limit of the control deviation is exceeded, an alarm routine is generated. Such redundant monitoring systems are commonly in use. However, they are associated with high cost, especially if there is a large number of similar control loops as is the case in controlling the temperature of textile machines like stretch winding machines or stretch twisting machines, where several hundred temperature control points with identical temperature setpoints are provided for each machine.